Simple Waves in Ideal Radiation Hydrodynamics

TL;DR

This paper analyzes simple wave solutions in ideal radiation hydrodynamics, demonstrating that in the dynamic diffusion limit, radiation behaves as an ideal fluid and providing analytical solutions for rarefaction waves.

Contribution

It extends hydrodynamic analysis to radiation fluids by replacing material parameters with radiative equivalents, offering analytical solutions and validation methods.

Findings

Analytical solutions for centered rarefaction waves in radiation hydrodynamics.

Validation of neglecting diffusion operator through numerical comparison.

Discovery that sound speed increases during rarefaction for fluids with many internal degrees of freedom.

Abstract

In the dynamic diffusion limit of radiation hydrodynamics, advection dominates diffusion; the latter primarily affects small scales and has negligible impact on the large scale flow. The radiation can thus be accurately regarded as an ideal fluid, i.e., radiative diffusion can be neglected along with other forms of dissipation. This viewpoint is applied here to an analysis of simple waves in an ideal radiating fluid. It is shown that much of the hydrodynamic analysis carries over by simply replacing the material sound speed, pressure and index with the values appropriate for a radiating fluid. A complete analysis is performed for a centered rarefaction wave, and expressions are provided for the Riemann invariants and characteristic curves of the one-dimensional system of equations. The analytical solution is checked for consistency against a finite difference numerical integration, and the validity of neglecting the diffusion operator is demonstrated. An interesting physical result is that for a material component with a large number of internal degrees of freedom and an internal energy greater than that of the radiation, the sound speed increases as the fluid is rarefied. These solutions are an excellent test for radiation hydrodynamic codes operating in the dynamic diffusion regime. The general approach may be useful in the development of Godunov numerical schemes for radiation hydrodynamics.